Two things come to my mind:
std::count_if and then compare the result to 1.
To avoid traversing the whole container in case eg the first two elements already match the predicate I would use two calls looking for matching elements. Something along the line of
auto it = std::find_if(begin,end,predicate);
if (it == end) return false;
++it;
return std::none_of(it,end,predicate);
Or if you prefer it more compact:
auto it = std::find_if(begin,end,predicate);
return (it != end) && std::none_of(std::next(it),end,predicate);
Credits goes to Remy Lebeau for compacting, Deduplicator for debracketing and Blastfurnance for realizing that we can also use none_of the std algorithms.